As always, Jones will have the final say on anything including any head coaching hires. However, the assumption all qualified head coaches would not accept a job offer from Jones is incorrect in my opinion.
A coach with significant NFL tenure at any level may be cautious about accepting a contract from Jones. I doubt that is the case for any coach who found success at the college level and wants to dip his toes in the big pond.
Riley can set up shop at Oklahoma. He has a good recruitment base along with full support of the university and a extremely loyal fanbase. He could make a lateral move at some point by going to another school and seek similar or better success. Or (if he is really ambitious) he could seek an NFL opportunity that presents itself and bypasses the coordinators' gig.
I doubt he would let Jones' reputation stop him from seizing the latter. If anything, Riley could strengthen his pro coaching resume in Dallas and find another landing spot in another NFL city should things fall apart.